I'm the only person that I know that is comfortable typing on the on-screen keyboard on an iPad, but I have now switched to a portable Bluetooth keyboard, mainly so that the keyboard no longer takes up half the screen.
Unlike most iPad keyboards, it is not part of my iPad's cover, but instead is a separate, ultrathin device which lies conveniently next to my iPad in my bag. It doesn't act as a stand, but if your iPad cover handles that, as mine does, that's not a problem.
It charges through a micro-USB the three or four times a year it needs charging and doubles as a keyboard for my phone and Apple TV at home (which doesn't work, but that's a whole other story). I was intending to get a keyboard that could switch between phone, tablet and desktop, but when I saw this much smaller product which would add virtually no bulk when traveling, I opted for it instead, and have been very pleased. With it, I often don't bother taking out my laptop when traveling, since I can do very nearly everything on the tablet, since even text entry is now quick.